Let X denote the number of times a certain nu- merical control machine will malfunction:

Let X denote the number of times a certain nu- merical control machine will malfunction: 1, 2, or 3 times on any given day. Let Y denote the number of times a technician is called on an emergency call. Their joint probability distribution is given as x
f(x,y) 1 2 3
1 0.05 0.05 0.15
y 3 0.10 0.10 0.35
5 0.20 0.10 3.54
A) Evaluate the marginal distribution of X.
B) Evaluate the marginal distribution of Y.
The joint density function of the random variables X and Y is
f(x,y)= 6x, 0 A) Show that X and Y are not independent.
B) Find P(X > 0.3|Y = 0.5). Let X, Y, and Z have the joint probability density function marginal distribution of Y.
C) Find P(Y = 3|X = 2).